Typically, atmospheric turbulence, such as caused by the weather, can cause degradation in the quality of images taken by telescopes and cameras. Several approaches have been used to deal with the problem of imaging through turbulence. In the area of astronomy, adaptive optics correct each frame by sensing the wavefront distortion induced by the turbulence and providing a servo-controlled phase screen, often referred to as a rubber-mirror. The use of such adaptive optics is described, for example, in H. W. Babcock, Publ. Astron. Soc. Pac. 65 (1953) 229, and R. K. Tyson, PRINCIPALS OF ADAPTIVE OPTICS, 1991. Imaging systems using adaptive optics to correct for atmospheric turbulence are complex and expensive.
Another approach for imaging through turbulence is speckle interferometry. Using a large sequence of frames taken at short exposure times through a telescope, the effect of atmospheric turbulence are reduced by processing the frames through Fourier transforms. Speckle interferometry is described, for example, in A. Labeyrie, Astron. Astrophys. 6 (1970) 85, K. T. Knox et al., “Recovery of Images from Atmospherically Degraded Short-Exposure Photographs,” Astrophys. J. 1993 (1974) L45, and F. Roddier, The effects of atmospheric turbulences in optical astronomy, in: Process in Optics XIX, 1981.
More recently, digital processing techniques are being used to correct images for atmospheric turbulence. In an article by B. R. Frieden, “An exact, linear solution to the problem of imaging through turbulence,” Opt. Comm. 150 (1998) 15, a sequence of two short-exposure intensity images is taken without any reference point sources, and the images are Fourier transformed and divided by linear equations based on two random point spread functions. The result is inverse filtered to provide an image of an object. One problem with this method is that the point spread function associated with the turbulence is not known in an image due to the lack of any reference, which can cause difficulty in recovering an image taken through turbulence. Accordingly, it would be desirable to more accurately recovery degraded images by using a reference point source or object in each image captured, which can be used to characterize the atmospheric turbulence as a point spread function.
In the area of digital image coding and compression, digital images may be processed as described in U.S. Pat. No. 5,453,844 using a random blurring function consisting of numerous, irregularly spaced delta functions. The patent provides for secure transmission of coded images.